Markov chain model of phytoplankton dynamics

Open access

Markov chain model of phytoplankton dynamics

A discrete-time stochastic spatial model of plankton dynamics is given. We focus on aggregative behaviour of plankton cells. Our aim is to show the convergence of a microscopic, stochastic model to a macroscopic one, given by an evolution equation. Some numerical simulations are also presented.

Adler, R. (1997). Superprocesses and plankton dynamics, Monte Carlo Simulation in Oceanography: Proceedings of the ‘Aha Huliko'a Hawaiian Winter Workshop, Manoa, HI, pp. 121-128.

Aldous, D. (1999). Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists, Bernoulli 5(1): 3-48.

Arino, O. and Rudnicki, R. (2004). Phytoplankton dynamics, Comptes Rendus Biologies 327(11): 961-969.

Clark, P. and Evans, F. (1954). Distance to nearest neighbor as a measure of spatial relationships in populations, Ecology 35(4): 445-453.

El Saadi, N. and Bah, A. (2007). An individual-based model for studying the aggregation behavior in phytoplankton, Ecological Modelling 204(1-2): 193-212.

Ethier, S. N. and Kurtz, T. G. (1986). Markov Processes: Characterization and Convergence, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, NY.

Franks, P. J. S. (2002). NPZ models of plankton dynamics: Their construction, coupling to physics, and application, Journal of Oceanography 58(2): 379-387.

Henderson, P. A. (2003). Practical Methods in Ecology, Wiley-Blackwell, Malden, MA.

Illian, J., Penttinen, A., Stoyan, H. and Stoyan, D. (2008). Statistical Analysis and Modelling of Spatial Point Patterns, John Wiley & Sons Ltd, Chichester.

Jackson, G. (1990). A model of the formation of marine algal flocs by physical coagulation processes, Deep-Sea Research 37(8): 1197-1211.

Laurençot, P. and Mischler, S. (2002). The continuous coagulation-fragmentation equations with diffusion, Archive for Rational Mechanics and Analysis 162(1): 45-99.

Levin, S. A. and Segel, L. A. (1976). Hypothesis for origin of planktonic patchiness, Nature 259.

Passow, U. and Alldredge, A. (1995). Aggregation of a diatom bloom in a mesocosm: The role of transparent exopolymer particles (TEP), Deep-Sea Research II 42(1): 99-109.

Rudnicki, R. and Wieczorek, R. (2006a). Fragmentation-coagulation models of phytoplankton, Bulletin of the Polish Academy of Sciences: Mathematics 54(2): 175-191.

Rudnicki, R. and Wieczorek, R. (2006b). Phytoplankton dynamics: from the behaviour of cells to a transport equation, Mathematical Modelling of Natural Phenomena 1(1): 83-100.

Rudnicki, R. and Wieczorek, R. (2008). Mathematical models of phytoplankton dynamics, Dynamic Biochemistry, Process Biotechnology and Molecular Biology 2 (1): 55-63.

Wieczorek, R. (2007). Fragmentation, coagulation and diffusion processes as limits of individual-based aggregation models, Ph.D. thesis, Institute of Mathematics, Polish Academy of Sciences, Warsaw, (in Polish).

Young, W., Roberts, A. and Stuhne, G. (2001). Reproductive pair correlations and the clustering of organisms, Nature 412(6844): 328-331.

International Journal of Applied Mathematics and Computer Science

Journal of the University of Zielona Góra

Journal Information


IMPACT FACTOR 2017: 1.694
5-year IMPACT FACTOR: 1.712

CiteScore 2018: 2.09

SCImago Journal Rank (SJR) 2018: 0.493
Source Normalized Impact per Paper (SNIP) 2018: 1.361

Mathematical Citation Quotient (MCQ) 2017: 0.13

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 176 145 11
PDF Downloads 48 43 4